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Let S=x,y|x2+y21,x0

Find the centroid of S.

Short Answer

Expert verified

Answer is43π,0

Step by step solution

01

Step 1. Given information

S=x,y|x2+y21,x0

02

Step 2. Explanation

S=x,y|x2+y21,x0

x¯=01-1-x21-x2xdydx01-1-x21-x2dydxx¯=01x[y]-1-x21-x2dx01[y]-1-x21-x2dx=201x1-x2dx2011-x2dx=01x1-x2011-x2dx=-131-x23/20112x1-x2+sin-1x01=13π4=43π

y¯=01-1-x21-x2ydydx01-1-x21-x2dydx=01y22-1-x21-x2dx01[y]-1-x21-x2dx=01[0]dx01[0]dx=0

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